轨道预报的一种乘法保辛摄动方法

发布时间：2018-03-19 00:07

本文选题：保辛　切入点：乘法摄动　出处：《中国科学:技术科学》2016年12期 　论文类型：期刊论文

【摘要】：为了准确预报人造卫星的轨道,需要考虑复杂的动力学模型,并使用数值方法进行求解.虽然Runge-Kutta法和Adams-Cowell法等数值积分方法在轨道预报中已经取得了预期的效果,但是一般不考虑保辛,忽视了系统的固有特性.本文提出适用于轨道预报的乘法保辛摄动方法,将描述卫星运动的Hamilton正则方程分解为二体问题和摄动部分.二体问题采用解析解,摄动部分用区段矩阵近似求解.由于二体问题的状态转移矩阵必然为辛矩阵,故此过程保辛.本文考虑的摄动因素有地球非球形引力、日月引力、太阳光压和潮汐摄动,选取GPS卫星做数值仿真,以GPS卫星精密星历为参照得到轨道预报误差,并与Runge-Kutta法和Adams-Cowell法进行对比.结果表明:对PRN01号GPS卫星和PRN02号GPS卫星进行3 d的轨道预报,本文算法的误差分别为4.56和10.10 m,精度与Runge-Kutta法和Adams-Cowell法一致,而Runge-Kutta法与Adams-Cowell法的计算耗时分别是本文算法的237.7%与71.3%,因此本文算法效率明显高于Runge-Kutta法,但比Adams-Cowell法稍低.
[Abstract]:In order to accurately predict the orbit of artificial satellites, complex dynamic models need to be considered and solved by numerical methods. Although numerical integration methods such as Runge-Kutta method and Adams-Cowell method have achieved the expected results in orbit prediction, However, the symplectic preserving method is not considered and the inherent characteristics of the system are ignored. In this paper, a multiplicative symplectic perturbation method suitable for orbit prediction is proposed. The Hamilton canonical equation describing the motion of a satellite is decomposed into two body problem and perturbation part. The analytic solution of the two body problem and the approximate solution of the perturbation part are adopted. The state transfer matrix of the two body problem must be a symplectic matrix. Therefore, the perturbation factors considered in this paper include the earth's non-spherical gravity, solar gravity, solar pressure and tidal perturbation. The GPS satellite is selected for numerical simulation, and the orbit prediction error is obtained by reference to the precise ephemeris of GPS satellite. Compared with Runge-Kutta method and Adams-Cowell method, the results show that the error of this method is 4.56 m and 10.10 m for PRN01 GPS satellite and PRN02 GPS satellite respectively, and the accuracy is consistent with Runge-Kutta method and Adams-Cowell method. The computational time of Runge-Kutta method and Adams-Cowell method are 237.7% and 71.3, respectively, so the efficiency of this method is obviously higher than that of Runge-Kutta method, but slightly lower than that of Adams-Cowell method.
【作者单位】：大连理工大学工业装备结构分析国家重点实验室;大连理工大学航空航天学院;大连理工大学工程力学系;
【基金】：国家自然科学基金(批准号:11372056,11432010)资助项目
【分类号】：V412.41

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